Related papers: Theory of Deep Convolutional Neural Networks II: S…
Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features,…
Recently there has been much interest in understanding why deep neural networks are preferred to shallow networks. We show that, for a large class of piecewise smooth functions, the number of neurons needed by a shallow network to…
Applications of neural networks to condensed matter physics are becoming popular and beginning to be well accepted. Obtaining and representing the ground and excited state wave functions are examples of such applications. Another…
In this paper, we provide a theoretical analysis of the inductive biases in convolutional neural networks (CNNs). We start by examining the universality of CNNs, i.e., the ability to approximate any continuous functions. We prove that a…
Convolutional neural networks (CNNs) constructed natively on the sphere have been developed recently and shown to be highly effective for the analysis of spherical data. While an efficient framework has been formulated, spherical CNNs are…
We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4x4 Ising model. Using its success at this task, we motivate the study of the larger 8x8 Ising model, showing that the…
We provide a mathematical interpretation of convolutional (or message passing) neural networks by using presheaves and copresheaves of the set of continuous functions over a topological space. Based on this interpretation, we formulate a…
Deep learning has established many new state of the art solutions in the last decade in areas such as object, scene and speech recognition. In particular Convolutional Neural Network (CNN) is a category of deep learning which obtains…
In this paper, we consider domain-invariant deep learning by explicitly modeling domain shifts with only a small amount of domain-specific parameters in a Convolutional Neural Network (CNN). By exploiting the observation that a…
Deep convolutional neural networks (CNNs) achieve remarkable performance on image classification tasks. Recent studies, however, have demonstrated that generalization abilities are more important than the depth of neural networks for…
Spherical convolutional neural networks (Spherical CNNs) learn nonlinear representations from 3D data by exploiting the data structure and have shown promising performance in shape analysis, object classification, and planning among others.…
In this paper, we propose a deep end-to-end neu- ral network to simultaneously learn high-level features and a corresponding similarity metric for person re-identification. The network takes a pair of raw RGB images as input, and outputs a…
The subject of deep learning has recently attracted users of machine learning from various disciplines, including: medical diagnosis and bioinformatics, financial market analysis and online advertisement, speech and handwriting recognition,…
We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…
We introduce a deep learning approach for analyzing the scattering function of the polydisperse hard spheres system. We use a variational autoencoder-based neural network to learn the bidirectional mapping between the scattering function…
Weight-sharing is ubiquitous in deep learning. Motivated by this, we propose a "weight-sharing regularization" penalty on the weights $w \in \mathbb{R}^d$ of a neural network, defined as $\mathcal{R}(w) = \frac{1}{d - 1}\sum_{i > j}^d |w_i…
Depth image super-resolution is an extremely challenging task due to the information loss in sub-sampling. Deep convolutional neural network have been widely applied to color image super-resolution. Quite surprisingly, this success has not…
Deep learning architectures based on convolutional neural networks tend to rely on continuous, smooth features. While this characteristics provides significant robustness and proves useful in many real-world tasks, it is strikingly…
Graph-structured data arise in many scenarios. A fundamental problem is to quantify the similarities of graphs for tasks such as classification. R-convolution graph kernels are positive-semidefinite functions that decompose graphs into…
Learning equivariant representations is a promising way to reduce sample and model complexity and improve the generalization performance of deep neural networks. The spherical CNNs are successful examples, producing SO(3)-equivariant…